Simplify to lowest terms. $\dfrac{54}{60}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 54 and 60? $54 = 2\cdot3\cdot3\cdot3$ $60 = 2\cdot2\cdot3\cdot5$ $\mbox{GCD}(54, 60) = 2\cdot3 = 6$ $\dfrac{54}{60} = \dfrac{9 \cdot 6}{ 10\cdot 6}$ $\hphantom{\dfrac{54}{60}} = \dfrac{9}{10} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{54}{60}} = \dfrac{9}{10} \cdot 1$ $\hphantom{\dfrac{54}{60}} = \dfrac{9}{10}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{54}{60}= \dfrac{2\cdot27}{2\cdot30}= \dfrac{2\cdot 3\cdot9}{2\cdot 3\cdot10}= \dfrac{9}{10}$